# How do you find the nth term in an arithmetic sequence?

## Question:

How do you find the nth term in an arithmetic sequence?

## Terminology of Arithmetic Sequences:

In mathematics, if a sequence, or list of numbers, is such that the difference between each consecutive term is constant, then we call the sequence an arithmetic sequence. We call the difference between each consecutive term of an arithmetic sequence the common difference of the sequence, and we represent the nth term of the sequence as an.

To find the nth term of an arithmetic sequence, we can use the following formula:

• an = a1 + (n - 1)d

In this formula, an is the nth term of the sequence, a1 is the first term of the sequence, and d is the common difference of the sequence.

For example, suppose we want to find the 25th term of the following arithmetic sequence.

• 4, 7, 10, 13, 16, 19, 22, . . .

To use our formula, we need the first term of the sequence, which is obviously 4, and we need the common difference of the sequence. To find the common difference, we simply find the difference between two consecutive terms of the sequence. Let's use the first and second term.

• Common difference = 7 - 4 = 3

We get that the common difference of the sequence is 3, so we plug n = 25, a1 = 4, and d = 3 into our formula, and simplify, to find the 25th term of the sequence.

• a25 = 4 + (25 - 1)(3) = 4 + (24)(3) = 4 + 72 = 76

We get that the 25th term of the given arithmetic sequence is 76.